Explain the principles of Maximum Likelihood Estimation (MLE). Also, explain the characteristics of an
estimator.

A random sample of 64 observations has a sample mean of 48 and a sample standard deviation of 10.
Find the following: 
 A 95% confidence interval for the population mean.
 Distinguish between point estimation and interval estimation.

 population has a mean of 80 and a standard deviation of 18. Random samples of size 64 are repeatedly
selected and reported. Compute the following for this: 

 Explain the Central Limit Theorem and discuss its significance in statistical inference. Illustrate how the
theorem helps in estimating population parameters when the population distribution is unknown.

 Explain the Uniform, Normal, Chi-square, t and F distributions. Highlight the relationships among these
distributions

The lifetime (in hours) of a sensor follows a normal distribution with a mean of 800 hours and a standard
deviation of 60 hours. Compute the following for this sensor:

Explain the Bernoulli, Binomial, Poisson and Hypergeometric distributions. Compare their assumptions,
parameters and applications.

A manufacturing process produces 2% defective products. A random sample of 25 products is selected.
Perform the following tasks for this process: (2 Marks)
 

Explain the concepts of joint probability mass function and marginal probability function for two discrete
random variables with the help of an example

A factory produces bulbs using two machines: (3 Marks)
 Machine A manufactures 60% of the bulbs, and 2% of the bulbs it produces are defective.
 Machine B manufactures 40% of the bulbs, and 5% of the bulbs produced by it are defective.
A randomly selected bulb is found to be defective. Using Bayes' theorem, determine the probability that
the defective bulb was manufactured by Machin

 If the letters of the word “Probability” are arranged randomly, what is the probability that all the letter ‘b’
are together in the random arrangement. 

Explain the concepts of skewness and kurtosis. A data scientist observes two datasets with the same mean
and variance but different skewness and kurtosis. Explain how these measures help in understanding the
nature of the distributions. Also, explain the characteristics of a normally distributed dataset

 The monthly sales (in lakh rupees) of a company for twelve months are: (4 Marks)
35, 42, 38, 41, 45, 39, 47, 50, 43, 44, 46, 40
Calculate:
 Range
 Variance
 Standard deviation
 Coefficient of variation
Comment on the sales pattern.

 Using the data given in Question 3, calculate: (5 Marks)
 Mean
 Median
 First Quartile (Q1)
 Third Quartile (Q3)
Draw a box plot and comment on the presence of any outliers.

The following marks (out of 100) were obtained by 30 students: (5 Marks)
42, 55, 67, 72, 48, 63, 59, 74, 81, 65, 58, 69, 77, 84, 71, 62, 57, 66, 73, 60, 75, 79, 68, 64, 53, 70, 61, 56,
76, 82
Construct:
 a frequency distribution,
 relative frequency table,
 histogram,
 ogive, and
 stem-and-leaf plot.

A researcher collects information on the following variables from 200 university students: (2 Marks)
 Gender
 Academic programme
 Annual family income
 Student satisfaction level (Very Low to Very High)
 CGPA
Identify the appropriate measurement scale (nominal, ordinal, interval or ratio) for each variable. Also,
explain the importance of selecting the correct measurement scale during statistical analysis.

A retail company wants to study customer purchasing behaviour in its stores. What would be the
population for this study be? How will you sample the data and draw inferences? Also, differentiate
between descriptive and inferential statistics with suitable examples

Conduct a field visit to a garment retail store to study the latest garment trends.
Analyze design features, including seam, stitches, pockets, collars, sleeves, and
plackets, and prepare a detailed report on your observations. 

Conduct a field visit to a garment retail store to study the latest garment trends.
Analyze design features, including seam, stitches, pockets, collars, sleeves, and
plackets, and prepare a detailed report on your observations. 

Develop a scrapbook displaying different trims, fasteners, sewing threads, and needles
commonly used in apparel manufacturing.

Body shape
b) Type of collars
c) Garment silhouette
d) Sizing system
e) Good fit
f) Parts of sleeve
g) Measuring tools